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Solutions question

2022 · 27 Jun · Shift 1 · Q1
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Solutions question

2022 · 27 Jun · Shift 1 · Q1

JEE MainChemistrySolutionsMCQ+4 / −1
Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : At 10 ∘^\circ∘ C, the density of a 5 M solution of KCl [atomic masses of K & Cl are 39 & 35.5 g mol −-− 1 respectively], is 'x' g ml −-− 1. The solution is cooled to −-− 21 ∘^\circ∘ C. The molality of the solution will remain unchanged. Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature. In the light of the above statements, choose the correct answer from the options given below :
  1. A
    Both (A) and (R) are true and (R) is the correct explanation of (A).
  2. B
    Both (A) and (R) are true but (R) is not the correct explanation of (A).
  3. C
    (A) is true but (R) is false.
  4. D
    (A) is false but (R) is true.
View written solutionFree

Correct answer: A

  1. Given data
  • Solution concentration = 5 M5\,\text{M}5M KCl
  • Temperature initially = 10∘C10^\circ \text{C}10∘C
  • Density at 10∘C10^\circ \text{C}10∘C = x g mL−1x\,\text{g mL}^{-1}xg mL−1
  • Final temperature = −21∘C-21^\circ \text{C}−21∘C
  • Molar mass of KCl = 39+35.5=74.5 g mol−139 + 35.5 = 74.5\,\text{g mol}^{-1}39+35.5=74.5g mol−1
  1. Understand molarity and molality
  • Molarity MMM = moles of solute per litre of solution
  • Molality mmm = moles of solute per kilogram of solvent

The assertion says that on cooling the solution, the molality remains unchanged.

  1. Check whether molality depends on temperature

Molality is defined as

m=moles of solutemass of solvent in kgm = \frac{\text{moles of solute}}{\text{mass of solvent in kg}}m=mass of solvent in kgmoles of solute​

Both:

  • moles of solute, and
  • mass of solvent

remain unchanged on changing temperature (provided no solute/solvent is lost and no phase separation/crystallization is implied).

Hence, molality does not change with temperature.

So the statement in the Reason (R) is true.

  1. Check the Assertion (A)

Even though the solution is cooled from 10∘C10^\circ \text{C}10∘C to −21∘C-21^\circ \text{C}−21∘C, the molality remains unchanged because molality depends on mass, not volume.

Therefore, Assertion (A) is true.

  1. Does Reason correctly explain Assertion?

Yes. The reason states exactly why molality remains unchanged:

  • mass is unaffected by temperature,
  • and molality depends on masses, not volume.

Thus, (R) is the correct explanation of (A).

  1. Option check
  • A: Both (A) and (R) are true and (R) is the correct explanation of (A). ✅
  • B: Incorrect
  • C: Incorrect
  • D: Incorrect

Therefore, the correct answer is A.

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